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The Stratonovich heat equation: a continuity result and weak approximations


 
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1. Title Title of document The Stratonovich heat equation: a continuity result and weak approximations
 
2. Creator Author's name, affiliation, country Aurélien Deya; Institut Élie Cartan, Nancy; France
 
2. Creator Author's name, affiliation, country Maria Jolis; Universitat Autònoma de Barcelona; Spain
 
2. Creator Author's name, affiliation, country Lluís Quer-Sardanyons; Universitat Autònoma de Barcelona; Spain
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) convergence in law; stochastic heat equation; Stratonovich integral; convolutional rough paths theory
 
3. Subject Subject classification 60H10; 60H05; 60H07
 
4. Description Abstract We consider a Stratonovich heat equation in $(0,1)$ with a nonlinear multiplicative noise driven by a trace-class Wiener process. First, the equation is shown to have a unique mild solution. Secondly, convolutional rough paths techniques are used to provide an almost sure continuity result for the solution with respect to the solution of the 'smooth' equation obtained by replacing the noise with an absolutely continuous process. This continuity result is then exploited to prove weak convergence results based on Donsker and Kac-Stroock type approximations of the noise.
 
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7. Date (YYYY-MM-DD) 2013-01-06
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/2004
 
10. Identifier Digital Object Identifier 10.1214/EJP.v18-2004
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 18
 
12. Language English=en en
 
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